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TIP OF THE RED GIANT BRANCH AS DISTANCE
INDICATOR
ESO KES, October 2019
Marina Rejkuba
Lemaitre
1927
Robertson
1928
Hubble
1929
Jan Oort
Sandage
Baade
Allan Sandage &
Gustav Tammann
Gerard de Vauculeurs
1996 Scale of the Universe debate:
Gustav Tammann vs Sidney van den Bergh
HST KEY PROJECT
• 1990 launch of the Hubble Space Telescope
• R. Giacconi (first director) established HST Key Projects:
1. Measure H0 with an accuracy of 10%
2. Study of the IGM through quasar absorption lines
3. Medium-deep survey of galaxies
2001: HST Key Program:
𝐻0 = 72 ± 8 𝑘𝑚 𝑠−1𝑀𝑝𝑐−1
Age of the Universe in the Einstein-de Sitter model: 9.1 Gyr
(still younger than some of the oldest stars)
Wendy Freedman
THE CARNEGIE-CHICAGO HUBBLE PROGRAM
RED GIANT BRANCH TIP THEORETICAL BACKGROUND
Solar composition tracks:
M= 0.9, 1, 1.2 …. 2.1 Mo
2.3, 2.5, 3 , 4, 5, 6 Mo
7 , 8 , 9 , 10 Mo
from BaSTI database
Dashed lines: constant radii
R=0.01,0.1,1,10,100,1000 Ro
Dot-dashed for WDs:
R= 0.008,0.013 Ro
(MWD=1,0.6 Mo)
Hot HB, AGB-Manque’,
normal HB tracks for
MHB=0.48,0.5,0.55 Mo
Stellar Evolutionary Tracks
PN
RED GIANT BRANCH EVOLUTION
RGB: He-core supported by e- degeneracy pressure surrounded by a H-burning shell that provides the luminosity
RGB evolution:
core mass increases → radius shrinks →
shell T & consequently the luminosity
generated in the shell increases → star
climbs along the RGB with increasing luminosity and core temperature
RGB Tip:
He core ignition → lifts e- degeneracy in the
core → core flash quenched within seconds → core inflates & star settles at lower
luminosity burning He in the core
H-R DIAGRAM FOR OLD STELLAR POPULATIONS
Stellar
evolutionary
tracks from
ZAMS to TRGB
for stars with masses: 0.8, 1,
and 1.3 M
i.e. age > 4 Gyr
Serenelli et al.
2017
Note:
Age-Metallicity
Degeneracy
RED GIANT BRANCH TIP
• Theoretically well understood: discontinuity for old metal-poor stars evolving on RGB
• Attractive alternative for RR Lyr & Cepheid distance scale
• Population II: lower extinction and crowding
• Single epoch observations – easy to observe/measure
• I-band TRGB nearly constant for old metal-poor stars
• 4 mag brighter than RR Lyr, less extinction than Cepheids
• Da Costa & Armandroff 1990 (DA90): “Standard Globular Cluster Giant Branches in the [MI vs (V-I)0] Plane”
• Lee, Freedman & Madore 1993: “The Tip of the Red Giant Branch as Distance Indicator for Resolved Galaxies”
DA COSTA & ARMANDROFF 1990: “STANDARD GLOBULAR CLUSTER
GIANT BRANCHES IN THE [MI VS (V-I)0] PLANE”
“In Sec. IV the cluster giant branch results are compared with the predictions of theory. … The agreement found is quite satisfactory
indicating, inter alia, that the giant branch tip luminosity can be used as a distance indicator for old stellar populations.”
MI assuming HB distances based on
Lee, Demarque & Zinn 1990 calibration:
MV(RR) = 0.82 + 0.17 [Fe/H]
DA90 Standard GC RGBs
𝐵𝐶𝐼 = 0.881 − 0.234 𝑉 − 𝐼 𝑇𝑅𝐺𝐵
𝑀𝑏𝑜𝑙𝑇𝑅𝐺𝐵 = −0.19
𝐹𝑒
𝐻−3.81
𝑚 −𝑀 𝐼 = 𝐼𝑇𝑅𝐺𝐵 − 𝑀𝐼,𝑇𝑅𝐺𝐵 = 𝐼𝑇𝑅𝐺𝐵 + 𝐵𝐶𝐼 −𝑀𝑏𝑜𝑙𝑇𝑅𝐺𝐵
𝑀𝐼 ≅ −4.05
𝐹𝑒/𝐻 = −15.16 + 17.0 𝑉 − 𝐼 −3 − 4.9 𝑉 − 𝐼 −32
LEE, FREEDMAN & MADORE 1993:“THE TIP OF THE RED GIANT
BRANCH AS A DISTANCE INDICATOR FOR RESOLVED
GALAXIES”
LEE ET AL. 1993
• Edge detection – zero sum Sobel Kernel [-2, 0, 2] convolution with I-band luminosity function
Madore & Freedman ‘95
LEE ET AL. 1993
• Method as in DA90 with slight modification:𝐹𝑒/𝐻 = −12.64 + 12.6 𝑉 − 𝐼 −3.5 − 3.3 𝑉 − 𝐼 −3.5
2
• Since 𝑀𝐼 ≅ −4 ± 0.1 𝑚𝑎𝑔 with little variation with metallicity for [Fe/H]≤ −0.7 dex, the method can be used up to ~4 Mpcfrom the ground and up to Virgo and Fornax with the HST
EARLY WORKS
• Sakai et al. 1996:
• replace the discrete LFs with their respective Gaussians (smooth)
• apply adaptive edge-detection – localised slope estimator with 4-point smoothing
• Madore & Freedman 1995: extensive computer simulations
• Signal-to-noise – larger than 5 to limit photometric errors
• Crowding – less than 25% (one star every 3 contaminated)
• Population size – need ~50 stars within upper 1 mag
• Contamination from non-RGB stars – work in outer halo
𝐸 𝑚 = Φ 𝐼 + ത𝜎𝑚 −Φ 𝐼 − ത𝜎𝑚
Sakai+1996: Sextans A
TRGB brightness in the main body 21.64
and in the halo 21.79
• Authors attribute to crowding
• Age may play a role as well
MEASURING TRGB
• Cioni et al. 2000
• LMC & SMC – TRGB in I, J, K band
• Bolometric correction using J-K color
• Using Savitzky-Golay filter to estimate the 2nd
derivative
• Use Gaussian fit to identify TRGB
• Systematic correction up to ~0.02 mag (AGB, photometric errors)
MAXIMUM LIKELIHOOD
• Mendez, B. et al. 2002, Makarov et al. 2006
• Maximum likelihood
• logarithmic edge detection to smooth the luminosity function
• RGB LF is a power law: 𝑁 𝑚 𝑑𝑚 ∝ 10𝑎𝑚 & 𝑎 = 0.30 ± 0.04
• Marginalising over free parameters: TRGB mag, LF slope brighter than TRGB, discontinuity strength
Makarov et al. 2006
TRGBDETECTION
Edge detection + smoothing due to
Poisson noise in the LF
Smoothing incorporated:
(i) in the edge detection of the kernel(ii) applied to the LF itself
(iii) folded in the model
Edge detection:
1. Discrete approx. to derivative (Sobel kernel)
2. Discrete approx. to derivative that
incorporate smoothing (Gaussian
formulation of Sobel kernel)
3. Maximum likelihood fitting
TRGB CALIBRATION
GCs: Ferraro+2000, Bellazzini+2004; Valenti+2004
Galaxies: Rizzi et al. 2007, Jang & Lee 2017
Bellazzini et al. 2004
Large dots:
Omega Cen
47 Tuc
Solid lines:
Empirical calibrations
Dashed lines:Fit to data
Open squares:
theoretical models
Salaris & Cassisi ‘98
RED GIANT BRANCH TIPNGC 5128
IRGBT=24.1± 0.1 mag
D = 3.8 ± 0.1 Mpc Rejkuba et al. 2005
I-BAND COLORDEPENDENT CALIBRATION
Rizzi et al. 2007:
• Slope is always the same
• Zero point calibrated via
HB in 5 Local Group
galaxies & applying
Carretta et al. 2000 calib
• MI = - 4.05 +/- 0.02 at
(V-I) = 1.6
TRGB: METALLICITY CORRECTION
𝑀𝐼𝑇𝑅𝐺𝐵 = 0.14
𝐹𝑒
𝐻
2
+ 0.48𝐹𝑒
𝐻− 3.629
𝑉 − 𝐼 = 0.581𝐹𝑒
𝐻
2
+ 2.472𝐹𝑒
𝐻+ 4.013
Belazzini et al. 2001, 2004:
Mager et al. 2008
Jang & Lee 2017
Quadratic fit to measure TRGB vs color
Zero point anchors:
• LMC (eclipsing binaries)
• NGC 4258 (Maser)
ERROR BUDGET
Jang & Lee
2017
aF555W – F814W to F606W – F814W transformation.
SUMMARY: I-BAND CALIBRATIONS
Beaton et al. 2018
TRGB IN INFRARED
Z = 0.004, 0.001, 0.004,
0.008, 0.19, and 0.30
Girardi+02 isochrones
NIR data for
24 GCs
Valenti + 2004
AGE DEPENDENCY
Salaris & Girardi 2005:
“… the TRGB method for distance determinations has to be applied with
caution to all galaxies that present signatures of intermediate-age stars.”
TRGB CALIBRATION WITH GAIA DR2
SkyMapper Gaia DR2 RGB with overplotted calibration of
the TRGB by Rizzi et al. 2007 (solid line)
Mould,
Clementini
& Da Costa
2019
BOLOMETRIC CORRECTION
Serenelli et al. 2017 𝑀𝐼𝑇𝑅𝐺𝐵 = 𝑀𝑏𝑜𝑙
𝑇𝑅𝐺𝐵 − 𝐵𝐶𝐼
Full age range
NGC 4258
THE CARNEGIE-CHICAGO HUBBLE PROGRAM
Extragalactic distance scale using only Population II distance indicators
Beaton+2018
Beaton et al. 2018
TAKE HOME MESSAGES
• TRGB potential for Cepheid-independent precise & accurate distance scale measurement
• TRGB as RELATIVE distance indicator – precision < 5%
• TRGB as ABSOLUTE distance indicator – accuracy > 5%
• Need better I-band bolometric corrections
• Future application for H0 measurements with ELT, JWST:
• K-band (and J, H) calibration work ongoing
• application possibly more complex
REFERENCES AND FURTHER MATERIAL
• Freedman, Wendy & Madore, Barry F., 2010, ARA&A: “The
Hubble Constant”
• Beaton, R. L., et al. 2018: “Old Aged Stellar
Population Distance Indicators”
• Serenelli, A, Weiss, A., Cassisi, S., et al., 2017: “The
brightness of the RGB tip. Theoretical framework, a set of
reference models, and predicted observables”